Convergent Stochastic Scalar Auxiliary Variable Method for Numerical Approximation of Nonlinear Stochastic Partial Differential Equations
The author proposes a new convergent stochastic scalar auxiliary variable (SSAV) method for the numerical approximation of nonlinear stochastic partial differential equations, using the stochastic Allen-Cahn equation as a prototype. The SSAV method allows for the derivation of linear, unconditionally stable, and convergent fully discrete schemes.
강성 상미분 방정식을 위한 적응형 시간 단계 반암시적 일단계 테일러 스킴
강성 및 비강성 성분을 통합된 프레임워크에서 안정성과 정확성을 보장하는 고차 암시적 및 반암시적 스킴을 제안한다.
Adaptive Time-Step Semi-Implicit One-Step Taylor Schemes for Solving Stiff Ordinary Differential Equations
This study proposes high-order implicit and semi-implicit schemes based on Taylor series expansion to efficiently solve stiff ordinary differential equations (ODEs) by handling stiff and non-stiff components within a unified framework, ensuring stability and accuracy.
Ensuring Numerical Reliability and Accuracy in Pipelined Bi-Conjugate Gradient Stabilized Method through ExBLAS Approach
The ExBLAS approach can provide reproducible and accurate results for the pipelined Bi-Conjugate Gradient Stabilized (p-BiCGStab) method, avoiding the need for residual replacement techniques.
Continuously Bounds-Preserving Discontinuous Galerkin Methods for Hyperbolic Conservation Laws
A novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving for any arbitrary choice of basis, approximation order, and mesh element type.
High-Performance Matrix-Free Evaluation of Unfitted Finite Element Operators
This work presents efficient matrix-free algorithms for evaluating the operator action in unfitted finite element discretizations, enabling high-performance computations with high-order polynomial spaces.
Efficient Numerical Methods for Solving Fokker-Planck Equations with Positivity Preservation
Fokker-Planck equations can be efficiently solved using the Chang-Cooper method combined with unconditionally positive and conservative Patankar-type time integration schemes, which preserve positivity and steady states.
Efficient Multiscale Coarse Approximations for Diffusion Problems in Perforated Domains
The authors propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain to efficiently solve diffusion problems in perforated domains. The coarse space is spanned by locally discrete harmonic basis functions with piecewise polynomial traces along the subdomain boundaries. The method provides superconvergence for a specific edge refinement procedure, even if the true solution has low regularity.
A Finite Element Method for Evolving Multi-Phase Interfaces with Triple Junctions
The authors introduce a structure-preserving finite element method for the numerical approximation of the multi-phase Mullins-Sekerka problem, which models the evolution of a network of curves driven by surface energy minimization and subject to area preservation constraints.
Dynamical Low-Rank Approximation of the Vlasov-Poisson Equation with Piecewise Linear Spatial Boundary
The core message of this article is to develop a projector splitting scheme for dynamical low-rank approximation (DLRA) of the Vlasov-Poisson equation that can handle inflow boundary conditions on spatial domains with piecewise linear boundaries.
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